High energy constraints in the octet SS-PP correlator and resonance saturation at NLO in 1/Nc

TL;DR

This paper investigates the octet SS-PP correlator using resonance chiral theory at next-to-leading order in 1/Nc, ensuring high-energy behavior matches the operator product expansion without relying on other observables, and refines low-energy constants.

Contribution

It provides a detailed NLO analysis of the octet SS-PP correlator in resonance chiral theory, deriving estimates for low-energy constants without using additional short-distance constraints.

Findings

Estimated L_8(mu)^{SU(3)} = (1.0+-0.4)×10^-3

Estimated C_{38}(mu)^{SU(3)} = (8+-5)×10^-6

Improved resonance chiral theory matching with chiral perturbation theory

Abstract

We study the octet SS-PP correlator within resonance chiral theory up to the one-loop level, i.e., up to next-to-leading order in the 1/Nc expansion. We will require that our correlator follows the power behaviour prescribed by the operator product expansion at high euclidian momentum. Nevertheless, we will not make use of short-distance constraints from other observables. Likewise, the high-energy behaviour will be demanded for the whole correlator, not for individual absorptive channels. The amplitude is progressively improved by considering more and more complicated operators in the hadronic lagrangian. Matching the resonance chiral theory result with chiral perturbation theory at low energies produces the estimates L_8(mu)^{SU(3)} = (1.0+-0.4)10^-3 and C_{38}(mu)^{SU(3)} = (8+-5) 10^-6 for mu=770 MeV. The effect of alternative renormalization schemes is also discussed in the article.